Propranolol pharmacokinetics in infants treated for Infantile Hemangiomas requiring systemic therapy: Modeling and dosing regimen recommendations

Abstract Propranolol has become the first choice therapy for complicated Infantile Hemangiomas (IH). The pharmacokinetics of propranolol were evaluated after repeated oral administration of a new pediatric solution of propranolol at 3 mg kg−1 day−1 given twice daily (BID) in infants (77‐243 days) with IH. A population model was built to describe the pharmacokinetics of propranolol in infants and to simulate different dosing regimens. One hundred and sixty‐seven plasma concentrations from 22 infants were used in the population analysis. Weight effect was tested on apparent clearance and volume of distribution. Monte‐Carlo simulations were performed for 4 dosing regimens: BID dosing with irregular or strict 12‐hour intervals and 2 different 3 time daily dosing (TID) regimens. The best model was a one‐compartment model with first‐order absorption and elimination rates. The weight affected the clearance but not the volume. Typical oral clearance was estimated at 3.06 L hour−1 kg−1 (95% CI: 1.14‐8.61 L hour−1 kg−1), close to adult clearance data. When regular BID dosing was compared to TID or irregular BID regimens, simulated median Cmin and Cmax were <20% different. To conclude, a model using a weight allometric function on clearance was established and confirmed that the dose in mg/kg should be used without adaptation by range of age in treatment of complicated IH. The simulations support the use of a BID dosing preferably to a TID dosing thanks to close Cmin and Cmax at steady state between both regimen and showed the possibility of irregular BID dosing, allowing early administration in the evening when needed.


| INTRODUCTION
Hemangiomas affect about 4% of all infants, and up to 30% of premature babies. Although 85%-90% of all infantile hemangiomas (IH) eventually undergo spontaneous involution, they can cause disfigurement and serious complications depending on their location (obstruction of airways and vision), size (cardiac insufficiency, hypothyroidism), and speed of regression. They can be associated with painful ulceration and hemorrhage. Treatment options for complicated hemangiomas include oral steroids, laser, surgery, cryotherapy, and vincristine, interferon or cyclophosphamide for lifethreatening cases. Each of these options has its restrictions and⁄or related side effects.
Since 2008, 22 propranolol has become the first choice therapy for complicated IH. 35 The current knowledge of mechanism of action of propranolol on IH evokes 3 possible concomittant mechanisms: vasoconstriction of the high-flow blood vessels feeding the IH tumor, VEGF growth factor suppression, and downregulation of other proangiogenic cytokines 15,35 Propranolol hydrochloride is a nonselective beta-adrenergic blocking agent. It has been in clinical use since the 1960's, and is commonly prescribed worldwide for cardiovascular diseases. In children, specific dosing recommendations have been established and its clinical use is accepted in hypertension, arrhythmias, tetralogy of Fallot spells, hypertrophic myocardiopathy, and thyrotoxicosis.
In adults, propranolol is almost completely absorbed after oral administration. 31 It undergoes a high first-pass metabolism by the liver and on average <30% of propranolol reaches the systemic circulation. 1,8,9 Maximum plasma drug concentrations (C max ) occur approximately 1-2 hours after an oral dose. 9,31,36,41 Approximately 90% of circulating propranolol is bound to plasma proteins. 12 Its volume of distribution is approximately 4 L kg À1 . 9,31 Propranolol is extensively metabolized through three primary routes: ring hydroxylation, side-chain oxidation, and direct glucuronidation involving mainly CYP2D6, CYP1A2, and UGT enzymes, respectively. Its halflife ranges from 3 to 6 hours. 8,9,36,41 Propranolol is excreted as metabolites in urine, <1% of a dose being excreted as unchanged drug in the urine. 39 In infants, limited information was available on the pharmacokinetic profile and plasma exposure of propranolol after oral administration. Until 2013, only 92 plasma concentrations observed after oral administration of propranolol in children from 8 weeks-to 13 years-old were documented in 3 publications: mean concentrations ranged between 0.05 and 57 ng mL À1 for different doses and regimen. 32,34,40 In 2013, 14 published results in 4 term and 23 preterm neonates treated with oral propranolol at 0.25 or 0.5 mg kg À1 every 6 hour in which 1000 concentrations were measured by serial dried blood spots. After 0.5 mg/kg/6 hour, the mean maximum concentrations were 71.7 AE 29.8 ng mL À1 .
A new pediatric oral solution of propranolol has been developed for the treatment of proliferative IHs requiring systemic therapy. Its efficacy has been demonstrated through one phase 2/3 dose ranging study at doses of 1 and 3 mg kg À1 day À1 with twice daily (BID) administration. 23 A pharmacokinetic study was also performed in the same infant population, in which plasma concentrations of propranolol were measured during the titration period and at steady-state at the target dose of 3 mg kg À1 day À1 given BID. Using these data, a population pharmacokinetic model was developed to describe the pharmacokinetics of propranolol in infants, to evaluate the between subjects variability (BSV) and as far as possible, to understand the source of the variability in this population. Finally, the population model was used to simulate different dosing regimens for supporting the administration of the propranolol solution in infants with IH. No statistical determination of sample size was performed. The study was designed to characterize the pharmacokinetics (PK) of propranolol at steady-state in infants administered with the pediatric oral solution. Infants were stratified to 2 groups according to their age at inclusion, which defined the timing of their PK assessment at steady-state:

| Study design
1. Group 1: infants aged from 35 to 90 days inclusive at inclusion; PK assessment after 4 weeks of treatment, 2. Group 2: infants aged from 91 to 150 days inclusive at inclusion; PK assessment after 12 weeks of treatment.
This stratification ensured to collect evaluable propranolol concentrations within the largest range of ages in a small group of infants. Twenty-three infants were enrolled from May 28th, 2010 to June 7th, 2011. The main criteria for inclusion were as follows: age at inclusion from 35 to 150 days old inclusive, and presence of proliferating IH requiring systemic therapy. Treatment was initiated with a titration period: the initial dose was 1 mg kg À1 day À1 for 1 week, then the dose increased to 2 mg kg À1 day À1 during the second week to achieve the target dose of 3 mg kg À1 day À1 for 10 weeks.
Treatment was given BID and was divided in 2 equal doses.
The dosing schedule was adapted to calculate an appropriate 12 hours exposure for the noncompartmental analysis (not shown) at the target therapeutic dose: in order to have a regular dosing time interval for the day of PK evaluation, it was requested to the parents that the evening administration before the day of full PK evaluation (D28 or D84) should be around 20:00 (last morning administration around 8:00) instead of around 17:00 for the other days. Available literature data did not allow to optimize the study design for the modeling approach. One-and two-compartment models were explored. In the one-compartment model, absorption was investigated using a zero-order and a first-order absorption rate. The distribution and elimination processes were parameterized in terms of volumes and clearances. As the absolute bioavailability could not be determined using only oral plasma data, apparent parameters were estimated.

| Pharmacokinetic assessments
BSV was investigated on all parameters. The magnitude of BSV was estimated with an exponential error model (Equation 1), which implies a lognormal distribution of parameters. It was expressed, approximately, as a coefficient of variation (CV%): where P j is the parameter for the jth individual, TVP is the population parameter and g j is the between-subject random effect having mean 0 and variance to be estimated x². were investigated to evaluate the residual error: where C ij is the observed value,Ĉ ij is the fitted value from the model, and e 1 and e 2 the random errors having mean 0 and variance to be estimated r².
Body weight, age or groups of age, sex, dose, and time were the key covariates assessed during the clinical study. However, regarding the covariate selection, some characteristics of the study design have had an impact in the modeling approach: 1. Stratification: Infants were stratified in 2 groups according to their age at inclusion. Infants of Group 2 being older than those of Group 1, the mean weight at inclusion was higher (4.77 kg vs. 6.38 kg).

Dose:
The target dose was expressed as mg/kg, and was individually calculated according to each infant weight.

3.
Timing of PK evaluation: The PK evaluation was performed at steady-state in both groups but after 4 weeks and 12 weeks of treatment for Group 1 and Group 2, respectively. At the PK evaluation time, the mean weight was 5.62 kg and 7.78 kg in Group 1 and Group 2, respectively.
Weight is the first covariate to be investigated in a pharmacokinetic modeling in infants in order to take into account the dose calculation in mg/kg and the growth and development of the infants. [17][18][19][20] As a consequence of the study design, the weight was highly correlated with the administered dose, the age and group of age, and the visit (time effect) ( Figure 1) and was the only tested covariate.
The weight was evaluated on the clearance and the volume of distribution using allometric functions 4,5,17,37 (Equation 4): where TVP i represents the model-predicted pharmacokinetic parameter (eg, total apparent plasma clearance CL/F) for the typical individual with covariate value cov i , P pop represents the population central tendency for TVP, cov med represents the median population value of the covariate, and h represents the allometric coefficient.

| Simulations of dosing regimens
The evaluation of propranolol pharmacokinetics was performed after fixing a regular 12 hour-dosing interval in order to calculate an appropriate AUC tau12 h for the noncompartmental analysis (not presented) and to decrease the unexplained variability in the modeling approach. On the contrary, in the phase 2/3 study, 23

F I G U R E 3 Propranolol base model: distributions of inter-individual variabilities inter-individual variability attached to apparent plasma clearance versus dose (A) visit number or time (D) weight (G) and age (J), inter-individual variability attached to apparent volume of distribution versus dose (B) visit number or time (E) weight (H) and age (K), interindividual variability attached to first-order absorption versus dose (C) visit number or time (F) weight (I) and age (L)
The 95% confidence interval (CI) of the random effect relative to V/F included 0.
Parameter estimates are provided in Table 4. The 95% CI of each parameter did not contain zero except random effect of V/F. The relative standard errors (RSE generated from the NONMEM covariance step) of fixed parameter estimates were <30% and <50% for random parameter estimates indicating a good precision of estimates except for V/F. 28

| Covariate selection and final model
Only a weight effect was tested on the structural parameters. During forward selection, the inclusion of weight affecting the clearance resulted in a significant decrease in the OFV of 12 units (P < .001).
The inclusion of weight effect on CL/F was performed by estimating the allometric exponent or by fixing the allometric exponent. AIC criteria was found lower using the allometric exponent fixed to 0.75 demonstrating that the exponent fixed to 0.75 is more appropriate.   Table 5.

| Visual predictive check
The 5th, 50 th , and 95th percentiles from the prediction corrected simulated data were superimposed with the observed concentrations in Figure 6 to visualize the predictive performance of the final PK model. Additional VPC performed by visit and coverage plots are given in Figures S1 and S2.

| Simulations
Propranolol concentrations were predicted for four dosing regimens by Monte-Carlo simulations (Figure 7).
Simulated median C max were compared for the BID administration with regular 12-hour dosing intervals and the alternative dosing regimens ( Table 6): differences were <10% with the BID administration 9-hour intervals and <5% for all the tested TID dosing regimens.
Simulated median C min showed a <20% differences between the regular 12-hour BID regimen and all the tested alternative dosing regimens.

| DISCUSSION
The main objectives of this analysis were to describe the pharmacokinetics of propranolol in infants, to evaluate the BSV and to understand the source of this BSV.
The analysis was performed using 167 concentrations data from 22 patients (6 males and 16 females) who were sampled twice during the titration period (1-2 mg kg À1 day À1 ) and 6 times during the target dose period (3 mg kg À1 day À1 ). The treatment was given BID.
A one-compartment model with a first-order absorption rate and a first-order elimination rate was the most appropriate model to describe the data. The BSV on the clearance, whatever the group of age, was around 40 %, which is close to that described in the literature for adult exposure. 21  techniques (ie, using body surface area), [3][4][5]37 Moreover it is recognized that a wide imprecision of empirical estimates of allometric exponents is obtained when estimated from typical sized datasets with limited numbers of subjects and distribution of weights means. 17 Finally, it was deemed that fixing the allometric exponent was an acceptable methodology.
Although it is recognized that a maturation model should be added in population PK models in infants to take into account the growth and the maturation of elimination/metabolism processes, one can conclude that for this specific model of propranolol in infants, the influence of ontogeny on the structural parameters was minimal for the considered period of age evaluated in this analysis. This could be explained by the characteristics of propranolol transformation which is balanced between several elimination pathways whose maturation rates are different. 2  The phase 2/3 dose ranging study has demonstrated the efficacy and tolerability of the new pediatric solution of propranolol at the dose of 3 mg kg À1 day À1 given BID. However, the available literature on the treatment of IH largely documented TID dosing regimen. 11,13,16,42 Considering that repeated administration of treatment in infants could not always be a regular dosing regimen (due to possible irregular sleeping periods and meal times), irregular BID dosing regimen and 2 different TID dosing regimens were simulated and compared with the regular BID dosing regimen investigated in the clinical PK study. Whatever the dosing regimen, simulations confirmed that infants are exposed to propranolol over a 24 hour-period. Simulated median C min and C max exhibit a <20% difference compared to the regular BID regimen.
With regard to safety, cardiovascular adverse events being known to be related with peak concentrations, the similarity between simulated C max after BID or TID daily dosing clears the risk of majored cardiovascular adverse events after BID dosing compared to TID dosing.
This has been confirmed during the phase 2/3 clinical study. T A B L E 6 5th, 50 th , and 95th percentiles of simulated C min and C max after repeated administration of 3 mg/kg/day of propranolol in infants Dosing regimen C min (ng/mL) C max (ng/mL)